Magnetic bearings are useful in a variety of applications in which a rotor is to be rotated in a contact-free manner. Applications of magnetic bearings include, e.g., turbo-molecular pumps (TMPs).
A rotor suspended in a magnetic bearing device for rotation around a rotor shaft can be described, to a first approximation, as a rigid object having six spatial degrees of freedom (DOFs). One DOF is the rotation around the device axis, whose direction will be designated as z in the following. This DOF is usually driven by an electromotor. Excitation of the other five degrees of freedom is undesired. These five degrees of freedom can be separated into three translational degrees of freedom (translational motions of the center of mass of the rotor in three directions x, y, and z, where x and y designate two mutually orthogonal axes perpendicular to the z direction) and two rotational degrees of freedom (tilting motions of the rotor around the x and y axes with fixed center of mass).
Control of these degrees of freedom is generally achieved by providing position and/or velocity sensors in various locations, feeding the sensor signals to a controller, and providing control signals for the actuators of the magnetic bearings at the controller outputs. At least five sensors are needed to control five degrees of freedom. Often, these sensors are: one sensor measuring displacements along the device axis (z); and two sensors each in an upper and a lower position along the device axis, for measuring displacements of an upper and a lower section of the shaft in the x and y directions.
A translational motion leads to the same displacement of both shaft sections. As an example, a translation in the x direction induces the same signal in an upper and a lower x sensor. A tilt leaves the center of mass unaffected and leads to different displacements of the upper and lower sections. A tilt, say, around the x axis leads to displacements in the y direction. In this sense, in this document reference to tilts “in” particular directions will be made: A tilt in a particular direction (called the tilt direction) is to be understood as a tilt in the plane spanned by the tilt direction and the z axis, or, equivalently, as a tilt around an axis (called the tilt axis) perpendicular to the tilt direction and the z axis. Mathematically, a tilt can be properly described by a tilt vector. The tilt vector is a unit vector pointing in the direction of the tilt axis, multiplied by the tilt angle.
In the controller, the signals from the upper and lower x and y sensors are transformed by forming weighted sums and differences to yield measures for translational displacements and/or velocities of the center of mass in the x and y directions, respectively, and for tilting displacements and/or angular velocities around the x and y axes, respectively. Traditionally, each of the three translational DOFs and the two tilting DOFs is then controlled separately by an individual control unit for each DOF. The outputs of these units are finally transformed back to generate driving signals for each actuator coil of the magnetic bearings. This control scheme can be readily generalized for the case where more than five sensors are employed. An example for such a traditional controller with ten sensor inputs organized in five pairs can be found in FIG. 2 of GB 2 109 596 A.
However, for rapidly rotating rotors, such a control scheme often does not achieve good results in controlling the tilting motions. One reason for this can be found in the gyroscopic character of the rotor. For a rigid rotor rotating at a high angular velocity, eigenmodes contributing to the tilting displacements are the precession and nutation modes. Precession and nutation are well-known effects in the theory of a rigid top; details can be found in standard textbooks of mechanics. The importance of these gyroscopic modes has been recognized in the art, and several approaches have been suggested for dealing with such gyroscopic effects. An important feature of the gyroscopic character of these modes is that a force in some direction may cause displacements in a different direction (or in other words, a moment of force around a given direction may cause angular displacements around a different direction). Therefore, a gyroscopic mode is properly controlled by applying forces not only in the opposite direction of a given displacement and/or velocity (say, along the x direction), but also in a direction perpendicular to the displacement resp. velocity (say, along the y direction).
In DE 33 23 648 A1, a cross-coupling scheme is proposed, in which an input signal for a tilt in the x direction does not only result in an output signal for the bearings in the x direction, but in which this input signal also causes an output signal in the y direction. Similarly, a tilt signal in the y direction also causes an output signal for the x bearings, however with opposite sign. In this way, the nutation mode can be controlled.
A similar scheme is proposed in GB 2 109 596 A. In that document the signs of the cross couplings are chosen opposite to DE 33 23 648 A1, such that the precession mode is controlled.
In EP 0 185 765, a cross-coupling scheme was proposed in which bandpass filters are employed in the cross-coupling branches. In this way, only tilting motions within a certain fixed frequency band lead to cross couplings. The frequency band is chosen such that the precession mode is identified by its frequency.
In U.S. Pat. No. 4,885,491 a control scheme employing cross couplings is disclosed, in which both a bandpass filter and a lowpass filter are employed in each cross-coupling branch, however, with opposite signs at their outputs. Additionally, the gain in the cross-coupling branches depends on the rotation frequency. This allows precession and nutation to be discriminated by their frequencies. Control is then performed dependent on the such-identified mode.
However, the control schemes of the prior art still often fail to achieve good, stable control at high rotation frequencies. This might be attributed to other disturbances superposed to a pure rigid-body behavior. This problem appears to be particularly strong in TMPs.
U.S. Pat. No. 4,697,128 employs a tracking filter at the rotational frequency for compensating unbalance vibrations of the rotor which are synchronous with the rotational frequency. As the tracking filter is centered at the rotational frequency, and only translational displacements are used as input signals, this method is only useful for unbalance compensation and cannot be applied for control of tilting motions.